How do you show that #f(x)=3-4x# and #g(x)=(3-x)/4# are inverse functions algebraically and graphically?

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Answer 1 · 2017-02-15T06:43:21

See proof below

To show that 2 functions are inverses, we calculate

#f(f^-1(x))# ant this is #=x#

Here, we have

#f(x)=3-4x#

#g(x)=(3-x)/4#

#f(g(x))=f((3-x)/4)=3-(4*(3-x)/4)=3-3+x=x#

#g(f(x))=g(3-4x)=(3-(3-4x))/4=(3-3+4x)/4=x#

Therefore,

#f(x)# and #g(x)# are inverses.

#QED#

Graphically, 2 functions are inverses if they are symmetric with respect to the line #y=x#

graph{(y-3+4x)(4y-3+x)(y-x)=00 [-3.7, 4.095, -0.95, 2.945]}